Inventory of "From Stargazers to Starships"

Sect. Concepts

1 Celestial sphere and its pole.
Equatorial and alt-azimuth mounting, coordinates.
2 The ecliptic and the zodiac.
Planets in the sky (also in #1)
2a Sundial construction
3 Seasons of the year and inclination of the Earth's axis.
4 Seasonal changes in the position of the Sun
4a The period of the Moon's orbit and the lunar month--why different.
How the moon revolves once a month.
The gravity-gradient force on the Moon.
4b Craters of the Moon--why round, why middle higher.
Loss of atmosphere by the Moon.
5 Latitude and Longitude.
Local and universal time
The International date line
Declination and right ascension, first point in Aries

6 Calendar: solar and sidereal day
Julian and Gregorian calendar
Lunar calendar--Metonic and Moslem.
7 Precession of the Earth, shift of pole star
Milankovich theory of ice ages.
8 Longitude and latitude
8a Why existence of horizon suggests the Earth curves.
8b Parallax, and its use estimating distances--to Moon, Stars, outdoors.
9a, 9b Aristarchus and his estimate of the size and distance of the Sun
9c Retrograde motion of inner and outer planets.
Ptolemy's theory of epicycles.
Copernicus model--planets overtaking or being overtaken.
10 Conic sections

11 Graphs, incl. circle and ellipse in (x,y) coords.
Example--drawing a specified ellipse.
Ellipse as collection of points with R1+R2 = const.
11a. Ellipse in polar coords. Orbital elements:
Semi-major axis, eccentricity.
Center of motion is not Sun but mutual center of gravity.
12. Intuitive concept of 2nd law--planet or satellite slows down when further away, relation to conservation of energy and analogy to motion of thrown stone.
12a Example of non-algebraic equation (Kepler's)
Concept of solving an equation by iteration [see M-2 for "Algorithm"]
Idea of orbital inclination, and that 2 more angles are needed to specify the orbit in 3 dimensions.
13 Acceleration, in particular acceleration g of free fall.
14 Concept of vector
vector addition and resolution into components.
15 Energy, kinetic, potential and other kinds. Conversion of energy from one kind to another, special role of heat [in 27, heat engines].

Sect. Calculations and formulas

2a (formulas for sundial--optional)
2a+ (reason why sundial must point at pole of the heavens--optional)
5a Finding one's lattitude using the pole star
Finding latitude using the noontime Sun
5b Cartesian and polar coordinates, in 2 and 3 dimensions (sine & cosine)

8 Calculation by Erastothenes of the Earth's size.
8a Distance to the horizon (use the theorem of Pythagoras)
8b Derivation of the parsec.
8c Calculation of the distance to the Moon by Aristarchus, using a total lunar eclipse
8d Calculation of the distance to the Moon by Hipparchus, using a total solar eclipse
9a Estimate of the distance and size of the Sun by Aristarchus, and how this might relate to his heliocentric theory.
9b The shadow-cone of the Earth.
10 Kepler's laws, formula for the 3rd law and examples from solar system.

21 Orbital and escape velocities.
Kepler's 3rd law for Earth satellites.
21a A practical equation for circular orbits around Earth, applied in 34.
22a Sweep-back of airplane wings
Operation of variable-pitch propeller on an airplane.
(this item & next illustrate frames of reference and resolution of vectors).
23 Variation of gravity observed from poles to equator. "Loop the loop"
on a roller coaster. Analysis in rotating and static frame.
24 Coriolis force due to Earth's rotation. Estimate effect in bathroom sink.
25 In 2-body interaction, center of gravity does not move.

26 Ballistic pendulum, used in determining the speed of a bullet.
27 Kinetic energy which needs to be dissipated in rocket re-entry.
30 Acceleration in a cannon for space launches.
Molecular veloc. inside cannon, reason for using hydrogen [also in 31]

M-1 Basic ideas of algebra: (1) unknown numbers can be handled as numbers. (2) Equal operations on both sides of equality create new equality.
M-3 Formulas--equations can be given only in symbols.
M-4 Identities: distributive law and its consequences.
M-5 Approximations with small quantities; Newton's binomial theorem.
M-6 Theorem of Pythagoras, proof by identities for the square of sum and difference.
M-7 Trigonometry: basic application, concept of baseline
M-8 Sines and cosines, sums of squares. (tan. & cotan., definition only)
M-9 Calculations: sines and cosines of complementary angles, derivation for angles of (30, 60), 45, (0, 90) and (15, 75) degrees.
M-10 Sines and cosines past 90 degrees, generalized using polar coordinates. Graph.
M-11 Sine and cosine of sum of angles.

Sect. Stories, extensions and illustrating examples

1 Psalm 19
4 Orientation of solar panels
Design of house windows, taking advantage of the Sun's motion.
4a Poem by Vachel Lindsay.
4b The story of exploration of the Moon using space vehicles.
5 Poem by John Masefield
5a Story of search for method to find longitude.
Story of Nansen getting lost, by losing the accurate time.
5b Rene Descartes

6 Lengthening of the day due to tides
Switch from Julian to Gregorian-- Washington's birthday, October Revolution.
7 Use of eclipses by Hipparchus to discover precession of equinoxes.
The evidence for ice ages on Earth.
The song "Dawning of the age of Aquarius" and its background.
8 Size of Earth as estimated by the ancients and by Columbus.
8a The story of Pike's Peak.
9a Story of Aristarchus, estimating the Sun's distance
and proposing the Earth went around the Sun.
9b Story of Copernicus.
Galileo and his first-ever astronomical telescope.
10 Story of Tycho and Kepler

11 Story of focusing of sound in old senate chamber.
11b Search for distant planets by wobble of star's position.
12 Jefferson's clock in Charlottesville.
13 Stories of Galileo and tower of Pisa,
Galileo using slanted board to study ball rolling under gravity
Cartoon depiction of gravity suddenly taking over is incorrect.
The way a gunsight works
Air resistance, and story of astronaut demonstrating free fall on Moon
15 Analogy of energy and money.
Calories in food.

16 Isaac Newton.
Examples of 3rd law: jumping from a boat, balancing a bicycle
17 Why mass explains the reason all bodies fall at the same rate.
Mass in the horizontal motion of a heavy wagon.
Measuring mass on the space station "Skylab," in "zero-g." Analogy to the balance spring on a wristwatch.
17a The complete story of mass measurement aboard "Skylab".
18 Roland Eötvös and the equality of gravitational and inertial mass.
(in 27, Eötvös and the high schools of Budapest)
20 Story of Newton's apple.

22a The aberration of starlight and how Bradley solved it.
Aberration of the solar wind, comet tails.
22b Problems of flight near the speed of sound.
24. NASA's simulation of weightlessness on an airplane.
26 History of rocket: Ft. McHenry, Tsiolkovsky, Goddard
Detailed story of Goddard: vision as teen ager. His use of a ballistic pendulum
Introduction of De-Laval nozzle, liquid fueled rocket.
27 History of rocketry--in Germany (V2) US. Von Braun, Oberth, Karman.
28 Stories of Sputnik and of Explorers 1 and 3.
29 Manned space flight--John Glenn, etc.
29a Spacecraft for astronomy--Hubble, etc. Links to sites.
29b Earth-monitoring spacecraft. Links to sites.
29c Spacecraft observing the Earth's outer environment. Links to sites.
29d Commercial use of space--comsats, GPS. Links to sites.
29e Planetary and lunar exploration by spacecraft. Links to sites.